This paper presents a generic probabilistic framework for estimating the statistical dependency and finding the anatomical correspondences among an arbitrary number of medical images. The method builds on a novel formulation of the $N$ -dimensional joint intensity distribution by representing the common anatomy as latent variables and estimating the appearance model with nonparametric estimators. Through connection to maximum likelihood and the expectation-maximization algorithm, an information-theoretic metric called $\mathcal {X}$ -metric and a co-registration algorithm named $\mathcal {X}$ -CoReg are induced, allowing groupwise registration of the $N$ observed images with computational complexity of $\mathcal {O}(N)$ . Moreover, the method naturally extends for a weakly-supervised scenario where anatomical labels of certain images are provided. This leads to a combined-computing framework implemented with deep learning, which performs registration and segmentation simultaneously and collaboratively in an end-to-end fashion. Extensive experiments were conducted to demonstrate the versatility and applicability of our model, including multimodal groupwise registration, motion correction for dynamic contrast enhanced magnetic resonance images, and deep combined computing for multimodal medical images. Results show the superiority of our method in various applications in terms of both accuracy and efficiency, highlighting the advantage of the proposed representation of the imaging process.

This article presents a general Bayesian learning framework for multi-modal groupwise image registration. The method builds on probabilistic modelling of the image generative process, where the underlying common anatomy and geometric variations of the observed images are explicitly disentangled as latent variables. Therefore, groupwise image registration is achieved via hierarchical Bayesian inference. We propose a novel hierarchical variational auto-encoding architecture to realise the inference procedure of the latent variables, where the registration parameters can be explicitly estimated in a mathematically interpretable fashion. Remarkably, this new paradigm learns groupwise image registration in an unsupervised closed-loop self-reconstruction process, sparing the burden of designing complex image-based similarity measures. The computationally efficient disentangled network architecture is also inherently scalable and flexible, allowing for groupwise registration on large-scale image groups with variable sizes. Furthermore, the inferred structural representations from multi-modal images via disentanglement learning are capable of capturing the latent anatomy of the observations with visual semantics. Extensive experiments were conducted to validate the proposed framework, including four different datasets from cardiac, brain, and abdominal medical images. The results have demonstrated the superiority of our method over conventional similarity-based approaches in terms of accuracy, efficiency, scalability, and interpretability.